Alice\'s RSA public key is P = (e, n) = (5, 65). Bob sends Alice the message by

Question

Alice's RSA public key is P = (e, n) = (5, 65). Bob sends Alice the message by encoding it as follows. The message only has upper-case letters and spaces. First he assigns numbers to characters: A Is 2, B is 3, ... , Z is 27, and blank is 28. Then he uses RSA to encode each number separately. Bob's encoded message is: Decode Bob's message. Notice that you don't have Bob's secrete key, so you need to "break" RSA to decrypt his message. For the solution, give Bob's message in plaintext (also, what does it mean and who said it?). You also need to describe step by step how you arrived at the solution. Suggestion: this can be solved by hand, but it will probably be faster to write a short program.

Explanation / Answer

n=65=5*13, thus phi(n)=(5-1)*(13-1)=48. Let c be an encrypted character. Then it decrypts to m=c^d mod n, where d=e^(-1) mod phi(n). d is 29 as 5*29=1 mod 48. so for example 21^29 mod 65 is 21, which translates to "T". THE QUESTION OF WHETHER A COMPUTER CNK IS NO MORE INTERESTING THAN THE QUESTION OF WHETHER A SUBMARINE CAN SWIM In Maple the code is T:=proc(x) if x=2 then print("A"); elif x=3 then print("B"); elif x=4 then print("C"); elif x=5 then print("D"); elif x=6 then print("E"); elif x=7 then print("F"); elif x=8 then print("G"); elif x=9 then print("H"); elif x=10 then print("I"); elif x=11 then print("J"); elif x=12 then print("K"); elif x=13 then print("L"); elif x=14 then print("M"); elif x=15 then print("N"); elif x=16 then print("O"); elif x=17 then print("P"); elif x=18 then print("Q"); elif x=19 then print("R"); elif x=20 then print("S"); elif x=21 then print("T"); elif x=22 then print("U"); elif x=23 then print("V"); elif x=24 then print("W"); elif x=25 then print("X"); elif x=26 then print("Y"); elif x=27 then print("Z"); elif x=28 then print(" "); fi; end; n:= 65; d := 29; T(((21)&^d) mod n); T(((29)&^d) mod n); T(((41)&^d) mod n); T(((58)&^d) mod n); T(((18)&^d) mod n); T(((42)&^d) mod n); T(((41)&^d) mod n); T(((50)&^d) mod n); T(((21)&^d) mod n); T(((30)&^d) mod n); T(((61)&^d) mod n); T(((45)&^d) mod n); T(((58)&^d) mod n); T(((61)&^d) mod n); T(((37)&^d) mod n); T(((58)&^d) mod n); T(((59)&^d) mod n); T(((29)&^d) mod n); T(((41)&^d) mod n); T(((21)&^d) mod n); T(((29)&^d) mod n); T(((41)&^d) mod n); T(((54)&^d) mod n); T(((58)&^d) mod n); T(((32)&^d) mod n); T(((58)&^d) mod n); T(((49)&^d) mod n); T(((61)&^d) mod n); T(((14)&^d) mod n); T(((62)&^d) mod n); T(((42)&^d) mod n); T(((21)&^d) mod n); T(((41)&^d) mod n); T(((54)&^d) mod n); T(((58)&^d) mod n); T(((49)&^d) mod n); T(((45)&^d) mod n); T(((12)&^d) mod n); T(((58)&^d) mod n); T(((30)&^d) mod n); T(((50)&^d) mod n); T(((58)&^d) mod n); T(((45)&^d) mod n); T(((61)&^d) mod n); T(((58)&^d) mod n); T(((14)&^d) mod n); T(((61)&^d) mod n); T(((54)&^d) mod n); T(((41)&^d) mod n); T(((58)&^d) mod n); T(((30)&^d) mod n); T(((45)&^d) mod n); T(((21)&^d) mod n); T(((41)&^d) mod n); T(((54)&^d) mod n); T(((41)&^d) mod n); T(((50)&^d) mod n); T(((21)&^d) mod n); T(((30)&^d) mod n); T(((45)&^d) mod n); T(((8)&^d) mod n); T(((58)&^d) mod n); T(((21)&^d) mod n); T(((29)&^d) mod n); T(((32)&^d) mod n); T(((45)&^d) mod n); T(((58)&^d) mod n); T(((21)&^d) mod n); T(((29)&^d) mod n); T(((41)&^d) mod n); T(((58)&^d) mod n); T(((18)&^d) mod n); T(((42)&^d) mod n); T(((41)&^d) mod n); T(((50)&^d) mod n); T(((21)&^d) mod n); T(((30)&^d) mod n); T(((61)&^d) mod n); T(((45)&^d) mod n); T(((58)&^d) mod n); T(((61)&^d) mod n); T(((37)&^d) mod n); T(((58)&^d) mod n); T(((59)&^d) mod n); T(((29)&^d) mod n); T(((41)&^d) mod n); T(((21)&^d) mod n); T(((29)&^d) mod n); T(((41)&^d) mod n); T(((54)&^d) mod n); T(((58)&^d) mod n); T(((32)&^d) mod n); T(((58)&^d) mod n); T(((50)&^d) mod n); T(((42)&^d) mod n); T(((48)&^d) mod n); T(((14)&^d) mod n); T(((32)&^d) mod n); T(((54)&^d) mod n); T(((30)&^d) mod n); T(((45)&^d) mod n); T(((41)&^d) mod n); T(((58)&^d) mod n); T(((49)&^d) mod n); T(((32)&^d) mod n); T(((45)&^d) mod n); T(((58)&^d) mod n); T(((50)&^d) mod n); T(((59)&^d) mod n); T(((30)&^d) mod n); T(((14)&^d) mod n);

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